Question

Janet rolls a standard $6$ -sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point her running total will equal $3?$

$\dfrac{2}{9}$

$\dfrac{49}{216}$

$\dfrac{25}{108}$

$\dfrac{17}{72}$

$\dfrac{13}{54}$

Answer: B

Concepts:dice (probability)casework

Difficulty rating: 1340

Solution:

The total can only reach exactly $3$ through the opening rolls, and these ways are disjoint: $3$ alone (probability $\frac16$ ), then $1,2$ and $2,1$ (each $\frac1{36}$ ), and $1,1,1$ (probability $\frac1{216}$ ). Add them up: $\frac{36}{216} + \frac{6}{216} + \frac{6}{216} + \frac{1}{216} = \frac{49}{216}.$ Thus, B is the correct answer.

2023 AMC 10A Problem 7

Answer: B

Difficulty rating: 1340

Solution:

Problem 7 in Other Years